Rodgers claimed Suarez’s qualities meant he should be valued in similar terms to Gareth Bale, the Tottenham forward who has attracted a near £100 million approach from Real Madrid.
Speaking after his side’s 2-2 draw with Napoli on the first day of the pre-season Emirates Cup tournament, Arsenal manager Wenger confirmed the club had made a formal bid for Suarez – believed to be in the region of £40 million.
But he also insisted negotiations would remain in-house and admitted he was perplexed by Rodgers’s decision to speak out.
“I do not understand this kind of thinking and would not like to talk openly about negotiations, because that is not my target in (this) press conference,” he said.
“We have one month in front of us and we will work very hard to strengthen our squad, without naming any specific names, because I do not believe that will make negotiations easier.
“After that, you can make all kind of thinking about the price of the players, and you can say as well they are all overboard anyway.
“I never said we have made a bid to Liverpool, now I can tell you we have made one, so at least that is some information. All the rest, I would like to keep to us.
“If we progress in that situation, we will inform you. At the moment, that is where we are.”
Wenger and his club’s board have once again come in for criticism in recent weeks after failing to secure any of their high-profile transfer targets, but the manager insists the club’s approach to conducting business will not change.
“When you want to buy any player, you need the agreement of the club, of the player and you need to agree a price, so you need three agreements,” Wenger said.
“It is like you go to your neighbour and say: ‘I want to buy your house, so get out tomorrow morning.’ He will not be necessarily happy about it.
“What is important is we focus on the players we have, that we are not too much drawn into these stories.
“I can understand they are interesting for people who love football, but it is not the most important (thing) in the game.
“We will treat every transfer with the rules we have always done until now, that is in a fair and respectful way.
“That is our club. That other clubs do differently is their problem, but we will be completely faithful to the values we think are important here.”
And asked if he believed his current squad could win the Premier League title, Wenger said: “Yes, of course. I am confident. Why should I sit here and say to you we can absolutely not win the title with the players we have?”
The Gunners trailed to first half goals from Lorenzo Insigne and Goran Pandev on Saturday before recovering after the interval to level through Olivier Giroud and an 87th minute equaliser from Laurent Koscielny.
Wenger, who hopes to conclude the sale of strikers Marouane Chamakh and Gervinho next week, said: “It was a good game overall at a good pace against a good side.
“I feel overall over 90 minutes we played going forward. It took us time to adjust defensively. And as well it was a good mental test because from two-nil down to come back for two-two is very impressive.”
Napoli manager Rafael Benitez was back in London for the first time since his departure from Chelsea at the end of last season after his spell as interim boss and he declared himself satisfied with his new side’s display.
“The game went well for us. We clearly showed what we wanted to do, how we wanted to play and were up to it,” Benitez said.